A mutant CTLA4 molecule comprising an extracellular domain of CTLA4 as shown in SEQ ID NO. 8 which begins with alanine at position 26 or methionine at position 27 and ends with aspartic acid at position 150, in which in the extracellular domain an alanine at position 55 is replaced with a tyrosine and a leucine at position 130 it is replaced with a glutamic acid, for use in the treatment of an immune disorder associated with graft transplantation, where the treatment comprises an early phase regimen and a maintenance phase regimen and where (i) the early phase regimen It varies from the first 3 to 6 months after the transplant and includes the administration of the mutant CTLA4 molecule to a subject on day 1, on the visit of week 2, the visit of week 4 and then monthly until the visit of the month 3 at a dosage of 10 mg / kg of the subject's weight, and (ii) the maintenance phase regimen begins after the end of the early phase regimen and implies administration with a non-frequent frequency. greater than once a month of an effective dose of the mutant CTLA4 molecule to a subject to provide a serum valley concentration of the mutant CTLA4 molecule of between about 0.2 mg / ml and about 3 mg / ml during the regimen of maintenance phase.Una molécula de CTLA4 mutante que comprende un dominio extracelular de CTLA4 como se muestra en SEQ ID NO. 8 que comienza con alanina en la posición 26 o metionina en la posición 27 y termina con ácido aspártico en la posición 150, en la que en el dominio extracelular una alanina en la posición 55 se sustituye con una tirosina y una leucina en la posición 130 se sustituye con un ácido glutámico, para uso en el tratamiento de un trastorno inmunitario asociado a trasplante de injerto, en donde el tratamiento comprende un régimen de fase temprana y un régimen de fase de mantenimiento y en donde (i) el régimen de fase temprana varía de los primeros 3 a los 6 meses después del trasplante y comprende la administración de la molécula de CTLA4
